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Find the equation of the plane which con...

Find the equation of the plane which contains the line of intersection of the planes `x+2y+3z-4=0a n d2x+y-z+5=0` and which is perpendicular to the plane `5x+3y-6z+8=0.`

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To find the equation of the plane that contains the line of intersection of the given planes and is perpendicular to another plane, we can follow these steps: ### Step 1: Identify the normal vectors of the given planes The equations of the planes are: 1. Plane 1: \( x + 2y + 3z - 4 = 0 \) → Normal vector \( \mathbf{n_1} = (1, 2, 3) \) 2. Plane 2: \( 2x + y - z + 5 = 0 \) → Normal vector \( \mathbf{n_2} = (2, 1, -1) \) 3. Plane 3: \( 5x + 3y - 6z + 8 = 0 \) → Normal vector \( \mathbf{n_3} = (5, 3, -6) \) ...
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Knowledge Check

  • The equation of the plane passing through the line of intersection of the planes x + 2y = 3 and y - 2z + 1 =0 and perpendicular to the first plane is

    A
    `2x - y - 10 z = 9`
    B
    `2x - y - 9z = 10`
    C
    `2x - y + 10 z = 11`
    D
    `2x - y + 7z =11`

  • The equation of the plane passing through the line of intersection of the planes x+y+z=6 and 2x+3y+4z+5=0 and perpendicular to the plane 4x+5y-3z=8 is

    A
    `x+7y+13z-96=0`
    B
    `x+7y+13z+96=0`
    C
    `x+7y-13z-96=0`
    D
    `x-7y+13z+96=0`

  • The equation of the plane passing through the line of intersection of the planes x+y+z=5 and 2 x + 3 y + 4z +5 = 0 and perpendicular to the plane x + y +z = 5 is

    A
    `x-z=10`
    B
    `x-z=20`
    C
    `x+y -2z=10`
    D
    `x+y -2z=20`

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    Find the equation of a plane containing the line of intersection of the planes x+y+z-6=0 and 2x+3y+4z+5=0 and passing through (1,1,1)

    Find the equation of the plane through the line of intersection of the planes x+y+z=1 and 2x+3y+4z=5 which is perpendicular to the plane x-y+z=0 Then find the distance of plane thus obtained from the point A(1,3,6) .

    Find the equation of a plane containing the line of intersection of the planes x+y+z-6 and 2x+3y+4z+5=0 passing through (1,1,1) .

    Find the equation of the plane through the line of intersection of the planes x+y+z=1 and 2x+3y+4z=5 , which is perpendicular to the plane x-y+z=0 . Also find the distance of the plane so obtained from the origin.

    Find the equation of the plane through the line of intersection of the planes x+2y+3z+4=0\ a n d\ x-y+z+3=0 and passing through the origin.

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